in a capillary tube with radius of .0008 m, a liquid of density 800 kg/m^3 and surface tension of 0.038 N/m in rising makes a contact angle of 60 with the tube wall. To height does the liquid rise?
To determine the height to which the liquid rises in a capillary tube, we can use the Young-Laplace equation, which relates the height (h) of the liquid column to the radius (r) of the tube, the contact angle (θ), the surface tension (σ), and the density (ρ) of the liquid.
The equation is given by:
h = (2σcosθ) / (ρgr)
Where:
h = height to which the liquid rises
σ = surface tension of the liquid
θ = contact angle
ρ = density of the liquid
g = acceleration due to gravity (approximately 9.8 m/s^2)
r = radius of the capillary tube
Now, let's substitute the given values into the equation:
σ = 0.038 N/m (surface tension)
θ = 60° (contact angle, but we need to convert it to radians)
ρ = 800 kg/m^3 (density)
g = 9.8 m/s^2 (acceleration due to gravity)
r = 0.0008 m (radius)
To convert the contact angle from degrees to radians, we use the formula: θ (radians) = θ (degrees) × (π/180)
θ (radians) = 60 × (π/180)
θ (radians) = π/3
Now, let's substitute all the values into the equation and solve for h:
h = (2 × 0.038 × cos(π/3)) / (800 × 9.8 × 0.0008)
cos(π/3) is equal to 0.5, so:
h = (2 × 0.038 × 0.5) / (800 × 9.8 × 0.0008)
Now, we can calculate the value of h:
h ≈ 0.000165 m
Therefore, the liquid rises to a height of approximately 0.000165 meters in the capillary tube.